Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 30000)	Who ?	When ?
9001	(74*10^54583+61)/9	54584	Robert Price	10/2015
9002	2^181316-94395	54582	Lelio R Paula	09/2011
9003	14751^5006+5006^14751	54572	Hans Havermann	08/2016
9004	14^47609+39	54567	Lelio R Paula	02/2013
9005	12696^13295-13295^12696	54559	Norbert Schneider	01/2018
9006	(2^124979+lucasV(2,-2,124979)+1)/3	54552	Paul Vanderveen	12/2017
9008	3^114327-74	54548	Lelio R Paula	10/2012
9007	(44*10^54547-161)/9	54548	Robert Price	11/2017
9009	gcd(V(995625),5F(199125)(F(199125)-1)+1)	54546	Serge Batalov	04/2015
9010	(17*10^54537-47)/3	54538	Robert Price	05/2017
9011	2^181155-1155*181155	54534	Henri Lifchitz	02/2005
9012	Phi(61672,83)	54533	Enzo Doria	05/2012
9013	(2*10^54527-197)/3	54527	Robert Price	11/2017
9014	9*2^181128+7	54526	Lelio R Paula	03/2014
9015	89*10^54518-7	54520	Robert Price	03/2017
9016	2^181090-113247	54514	Enzo Doria	07/2014
9017	14031^7670+7670^14031	54508	Hans Havermann	08/2016
9018	14210^6849+6849^14210	54505	Hans Havermann	08/2016
9019	2^181043-199	54500	Lelio R Paula	02/2011
9020	12^50499+5	54498	Lelio R Paula	01/2013
9021	12^50491+5	54489	Lelio R Paula	01/2013
9022	6^70016-145	54484	Lelio R Paula	10/2012
9023	11^52313-9600	54479	Enzo Doria	02/2013
9024	2^64459+3^64459+5^64459+7^64459	54475	Henri Lifchitz	08/2001
9025	2^180946-111041	54471	Enzo Doria	05/2014
9026	(64*10^54467+287)/9	54468	Robert Price	04/2016
9027	(32*10^54458+319)/9	54459	Robert Price	10/2017
9028	5^77907-2*3^77907	54455	Mike Oakes	11/2009
9029	20^41853-5623	54453	Enzo Doria	03/2013
9030	14^47506-75	54448	Lelio R Paula	02/2013
9031	(25*10^54443-67)/3	54444	Robert Price	11/2017
9032	2^180839-113437	54438	Enzo Doria	08/2014
9033	3^114085+28	54433	Lelio R Paula	10/2012
9034	Phi(141230,10)	54432	Ray Chandler	08/2009
9035	6^69946-55	54429	Lelio R Paula	10/2012
9036	p(11796)#/2-1024	54427	Robert Price	09/2017
9037	5*2^180796+3	54426	Lelio R Paula	03/2014
9038	(23*2^180782-1)/91	54421	Lelio R Paula	01/2014
9039	9*6^69928-7	54416	Lelio R Paula	09/2014
9040	92^27701-91^27701	54399	Robert Price	08/2015
9041	(2^180687-3)*6-7	54393	Gilbert Mozzo	04/2016
9042	(5*10^54388-11)/3	54389	Erik Branger	12/2013
9043	20^41799-3043	54382	Enzo Doria	03/2013
9044	13860^8387+8387^13860	54382	Hans Havermann	08/2016
9045	(F(19)^15017-F(18)^15017)/F(17)	54378	Wayne Halsdorf	05/2010
9046	7^64329-18	54365	Lelio R Paula	10/2012
9047	2^180551-967	54352	Yves Minet	01/2012
9048	15^46209-74	54347	Lelio R Paula	02/2013
9049	10^54345+29739	54346	Patrick De Geest	08/2013
9050	10^54345-141381	54345	Patrick De Geest	09/2013
9051	lucasU(2098,1,16360)-lucasU(2098,1,16359)	54342	Mike Oakes	05/2009
9052	177^24171-2	54336	Lelio R Paula	10/2017
9053	2^180496+15	54335	Lelio R Paula	02/2011
9054	1845^16636+16636^1845	54334	Serge Batalov	05/2014
9055	11^52169-70	54329	Lelio R Paula	01/2013
9056	2^180446-4031	54320	Yves Minet	02/2018
9057	13693^9262+9262^13693	54317	Hans Havermann	06/2016
9058	2^180429-113101	54315	Enzo Doria	07/2014
9059	2^180423-112051	54313	Enzo Doria	05/2014
9060	16112^2349+2349^16112	54312	Hans Havermann	06/2016
9061	(79^28621-1)/78	54311	Paul Bourdelais	08/2017
9062	(13^48751+4^48751)/17	54305	Robert Price	05/2013
9063	2^180370+12915	54297	Lelio R Paula	09/2012
9064	(10^54290+41)/3	54290	Robert Price	01/2017
9065	15108^3917+3917^15108	54283	Hans Havermann	06/2016
9066	2^180317-3019	54281	Yves Minet	10/2014
9067	2^180314+855	54280	Lelio R Paula	10/2009
9068	19^42425+94	54252	Lelio R Paula	02/2013
9069	2^180180-1005449	54240	Paul Bourdelais	11/2012
9070	2^180173-2773	54238	Yves Minet	07/2014
9071	13367^11418+11418^13367	54238	Hans Havermann	06/2016
9072	427^20614+20614^427	54224	Norbert Schneider	06/2016
9073	2^180124-87959	54223	Gary Barnes	08/2009
9074	2^180111-113101	54219	Enzo Doria	07/2014
9075	2^180101-114871	54216	Enzo Doria	05/2015
9076	(11*2^180099+1)/51617	54212	Lelio R Paula	07/2012
9077	2^180070+465	54207	Lelio R Paula	09/2012
9078	13683^9154+9154^13683	54207	Hans Havermann	06/2016
9079	8105225132^180009-95312^9531-1	54198	Jiong Sun	12/2003
9080	2^180014+613	54190	Jason Earls	04/2008
9081	2^180007+101	54188	Lelio R Paula	02/2011
9082	2^180001+41877	54186	Jim Fougeron	08/2002
9083	2^180000+130153	54186	Jim Fougeron	09/2002
9084	3^113565-74	54185	Lelio R Paula	10/2012
9085	50^31891-49	54182	Norbert Schneider	07/2014
9086	(5*2^179991-1)/11427	54180	Lelio R Paula	01/2014
9087	3^113548+26	54177	Lelio R Paula	10/2012
9088	(lucasV(1,2,360029)-2)/(3^3522251725981)	54177	Mike Oakes	04/2017
9089	181^23996-2	54176	Lelio R Paula	10/2017
9090	4159^14969-138	54173	Enzo Doria	07/2012
9091	2^179955+5775	54172	Lelio R Paula	10/2009
9092	2^179953-231313	54172	Enzo Doria	05/2014
9093	5^77485+6	54160	Lelio R Paula	10/2012
9094	18^43141+85	54154	Lelio R Paula	02/2013
9095	10^54149+187647	54150	Patrick De Geest	07/2017
9098	3^113489-340	54149	Lelio R Paula	10/2012
9096	10^54149-800001	54149	Robert Price	06/2017
9097	10^54149-36501	54149	Patrick De Geest	07/2017
9099	7^64070+90	54146	Lelio R Paula	10/2012
9100	12549^13210-13210^12549	54143	Norbert Schneider	12/2017
9101	18^43131+71	54142	Lelio R Paula	02/2013
9102	2^179826-131	54134	Lelio R Paula	02/2011
9103	2^179815-112735	54130	Enzo Doria	06/2014
9104	2^179806+73849	54127	Enzo Doria	04/2016
9105	2^179790+33	54123	Donovan Johnson	02/2006
9106	14287^6138+6138^14287	54120	Hans Havermann	06/2016
9107	(17*10^54117+1)/9	54118	Serge Batalov	05/2010
9108	2^179763-189	54115	Lelio R Paula	02/2011
9109	(21181*2^179770+1)/3029105	54115	Lelio R Paula	05/2014
9110	1828^16589+16589^1828	54113	Serge Batalov	05/2014
9112	20^41588-5883	54108	Enzo Doria	03/2013
9111	50^31847-49	54108	Norbert Schneider	07/2014
9113	2^179733-6855	54106	Lelio R Paula	10/2009
9114	20^41584-5583	54103	Enzo Doria	03/2013
9115	10^54084+3*3^54084	54085	Mike Oakes	05/2010
9116	2^179613-1795	54069	Lelio R Paula	10/2009
9117	2^179589-1011523	54062	Paul Bourdelais	11/2012
9118	2^179574-2531	54058	Yves Minet	07/2014
9119	(41*10^54051-23)/9	54052	Robert Price	05/2015
9120	117^26131-116	54044	Norbert Schneider	10/2013
9121	(10^54038-31)/3	54038	Serge Batalov	12/2014
9122	11^51885-84	54033	Lelio R Paula	01/2013
9123	14990^4011+4011^14990	54013	Hans Havermann	07/2016
9124	(19*2^179414+1)/7	54010	Lelio R Paula	07/2012
9125	3^113182-10408	54002	Enzo Doria	02/2013
9126	35^34970-8786	53997	Enzo Doria	03/2013
9127	2^179371-1637587	53997	Enzo Doria	05/2015
9128	19^42225-92	53996	Lelio R Paula	01/2013
9129	10190^13471-13471^10190	53995	Norbert Schneider	05/2018
9130	(3^113188+7)/73917675784	53994	Lelio R Paula	03/2012
9131	7*3^113162+8	53993	Lelio R Paula	03/2014
9132	(10^53991+179)/9	53991	Serge Batalov	12/2014
9133	2^179350-2145	53990	Lelio R Paula	10/2009
9134	(-lucasV(1,2,358718)-2)/(51719)	53990	Mike Oakes	04/2017
9135	8^59782-6^59782-3^59782	53989	Mike Oakes	11/2009
9136	3*7^63861+8	53970	Lelio R Paula	09/2014
9137	2^179274+71389	53967	Enzo Doria	04/2016
9138	2^179259-58695	53963	Lelio R Paula	10/2009
9139	6^69345+61	53961	Lelio R Paula	10/2012
9140	(-lucasV(1,2,358635)+2)/(71793172321719602511716271)	53957	Mike Oakes	04/2017
9141	(40216^11719-1)/40215	53955	Serge Batalov	04/2015
9142	89*10^53951-9	53953	Robert Price	05/2017
9143	14^47067-3	53945	Lelio R Paula	01/2013
9144	p(11700)#/2-512	53937	Robert Price	07/2017
9145	(2^179168-5)/59	53934	Lelio R Paula	02/2012
9146	2^179128+8415	53923	Lelio R Paula	07/2012
9147	2^179120+2533	53921	Henri Lifchitz	09/2004
9149	(2^179126+78557)/4649321187	53913	Lelio R Paula	05/2012
9148	74^28842+73	53913	Norbert Schneider	11/2012
9150	1271^17368+17368^1271	53913	Serge Batalov	05/2014
9151	2^179079+53	53909	Lelio R Paula	02/2011
9152	17^43807+54	53903	Lelio R Paula	01/2013
9153	17^43807+30	53903	Lelio R Paula	01/2013
9154	3^112951-310	53892	Lelio R Paula	10/2012
9155	Phi(7,2957!)	53888	Robert Price	05/2015
9156	(10223*2^178975+1)/33985	53877	Lelio R Paula	05/2014
9157	2^178944-219209	53868	Enzo Doria	11/2012
9158	(10^53859+149)/3	53859	Serge Batalov	12/2014
9159	2^178910-191	53858	Lelio R Paula	02/2011
9160	16170^2141+2141^16170	53857	Hans Havermann	07/2016
9161	(5*10^53855-107)/3	53856	Robert Price	01/2017
9162	(72*10^53847-27)/99	53847	Patrick De Geest	08/2004
9163	2^178841-869688105	53837	Lelio R Paula	06/2012
9164	2*10^53834-27	53835	Robert Price	02/2017
9166	2^178821-1011523	53831	Paul Bourdelais	11/2012
9165	12601^13128-13128^12601	53831	Norbert Schneider	10/2017
9167	2^178819-15	53830	Lelio R Paula	02/2011
9168	(14450!-1)/225296581	53829	Donovan Johnson	04/2006
9169	(124351#+125386)/(2^57188344891039820259)	53826	Makoto Morimoto	10/2017
9170	10530^13381-13381^10530	53825	Norbert Schneider	03/2018
9171	2^178761-465	53813	Lelio R Paula	10/2009
9172	18900^703+703^18900	53808	Anatoly F. Selevich	02/2007
9173	13918^7343+7343^13918	53806	Hans Havermann	08/2016
9174	10^53804+31749	53805	Patrick De Geest	12/2012
9175	10^53804-71	53804	Robert Price	05/2011
9176	t(178994)	53804	Robert Price	03/2015
9177	(2^178693-lucasV(1,2,178693)+1)/2	53792	Mike Oakes	11/2016
9178	2^178671-113215	53786	Enzo Doria	07/2014
9179	15110^3621+3621^15110	53774	Hans Havermann	07/2016
9180	2^178611+95	53768	Lelio R Paula	02/2011
9181	2^178597+5711	53764	Lelio R Paula	10/2011
9182	2^178598+12915	53764	Lelio R Paula	07/2012
9183	(9179*2^178579-1)/303	53760	Lelio R Paula	03/2015
9184	10671^13342-13342^10671	53745	Norbert Schneider	02/2018
9185	5*7^63589+2	53740	Lelio R Paula	09/2014
9186	2^178516-112515	53739	Enzo Doria	06/2014
9187	20^41302-27	53736	Lelio R Paula	01/2013
9188	6^69054-39209	53735	Mike Oakes	12/2010
9189	13086^12769+12769^13086	53734	Hans Havermann	07/2016
9190	2^178455+76043	53721	Enzo Doria	04/2016
9191	(10^53718-7)/3	53718	Makoto Kamada	10/2004
9192	(67607*2^178426+1)/3	53716	Lelio R Paula	05/2014
9193	9*10^53707+11	53708	Robert Kinser	01/2017
9194	94601!8-2	53708	Robert Price	04/2017
9195	13214^11595+11595^13214	53706	Hans Havermann	07/2016
9196	Phi(134350,10)/537401/8011962251	53705	Maksym Voznyy	10/2011
9197	2^178367-379	53694	Yves Minet	03/2013
9198	(2^178364-5)/11	53692	Lelio R Paula	02/2012
9199	4339^14760-168	53688	Enzo Doria	06/2012
9200	12^49746-11	53685	Lelio R Paula	01/2013
9201	12950^13051-13051^12950	53670	Norbert Schneider	08/2017
9203	(9913*2^178266-1)/2247	53665	Lelio R Paula	03/2015
9202	13725^8128+8128^13725	53665	Hans Havermann	07/2016
9204	2^178250-113261	53659	Enzo Doria	07/2014
9205	2^178226+11715	53652	Lelio R Paula	10/2009
9206	35^34742-1976	53645	Enzo Doria	03/2013
9207	20^41228-563	53639	Enzo Doria	03/2013
9208	359^20992+20992^359	53637	Norbert Schneider	08/2014
9209	(27*2^178183-1)/29065	53636	Lelio R Paula	01/2014
9210	(3^112414+7)/37381696	53628	Lelio R Paula	03/2012
9211	17994^955+955^17994	53623	Anatoly F. Selevich	10/2006
9212	2^178117-1551	53619	Yves Minet	08/2012
9213	2^178099-11287	53614	Enzo Doria	06/2014
9214	10751^13298-13298^10751	53611	Norbert Schneider	01/2018
9215	(15*2^178080-1)/309071	53604	Lelio R Paula	01/2014
9216	5^76672-13766	53592	Enzo Doria	02/2013
9217	6^68868-137	53590	Lelio R Paula	10/2012
9218	(5*2^178021+1)/8173	53587	Lelio R Paula	07/2012
9219	5^76654-26	53579	Lelio R Paula	10/2012
9220	(3^112297-2)/7627	53576	Lelio R Paula	03/2012
9221	3*2^177948-7	53569	Lelio R Paula	03/2014
9222	10^53558+18543	53559	Patrick De Geest	12/2012
9223	10^53558-21	53558	Robert Price	03/2011
9224	2^177792-95	53521	Lelio R Paula	02/2011
9225	13392^9919+9919^13392	53521	Hans Havermann	07/2016
9226	13105^12132+12132^13105	53520	Hans Havermann	07/2016
9227	13^48042+82	53517	Lelio R Paula	01/2013
9228	2^177768+39121	53514	Yves Minet	10/2010
9229	13835^7366+7366^13835	53504	Hans Havermann	07/2016
9230	17^43477+84	53497	Lelio R Paula	01/2013
9231	5*10^53492+9	53493	Dmitry Domanov	11/2010
9232	2^177683+95	53488	Lelio R Paula	01/2011
9233	11057^13226-13226^11057	53482	Norbert Schneider	12/2017
9234	(2^177678+3)/514627	53481	Lelio R Paula	02/2012
9235	2^177641-255463	53476	Gary Barnes	08/2009
9236	p(11608)#/2+16	53469	Robert Price	12/2016
9237	(14*10^53465+211)/9	53466	Robert Price	11/2017
9238	37302#*10^(37302+52)+p(37302+1)	53457	Jason Earls	08/2008
9239	12001^13104-13104^12001	53455	Norbert Schneider	10/2017
9240	1829^16384+1828^16384	53449	Henri Lifchitz	01/2007
9241	10^53442+12621	53443	Patrick De Geest	06/2018
9242	10^53442-2007	53442	Patrick De Geest	06/2018
9243	35^34608-9602	53438	Enzo Doria	03/2013
9244	(3^111992+8)/14867	53430	Lelio R Paula	03/2012
9246	2^177480+1869661	53427	Enzo Doria	05/2016
9245	11791^13122-13122^11791	53427	Norbert Schneider	10/2017
9247	(8*10^53411+1)/9	53411	Serge Batalov	12/2008
9248	4*5^76410-3	53409	Lelio R Paula	09/2014
9249	2^177380-113045	53397	Enzo Doria	07/2014
9250	5^76362-2*3^76362	53375	Mike Oakes	11/2009

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Probable Primes Top 10000

(212140 PRPs in the top)